Observations from Z-Score Visualization
Mean (µ) is shown as a black dot on each line and marked with a
vertical dashed line for reference.
Each data point is plotted on its own horizontal line, showing its
distance from the mean.
Z-scores are annotated beside each point, indicating how many
standard deviations away the point is from the mean.
Points within µ ± 2σ are marked in green, indicating they fall within
the typical range of a normal distribution.
Points beyond µ ± 2σ are marked in red, indicating they are
statistical outliers.
Vertical dashed lines mark standard deviation levels: µ ± 1σ, µ ± 2σ,
and µ ± 3σ, helping to contextualize where each point lies.
A point near 85 lies just beyond µ + 3σ, a rare event (occurs in less
than 0.15% of data in a standard normal distribution).
Similarly, points like 20 and 25 fall below µ − 2σ, also considered rare
in a normal distribution.